Abstract

This study applies terms and methods for describing spatial interactions between multivariate spatial point patterns, which are, to our knowledge, new in neurobiology. We consider two categories of points, type 1 and 2, distributed within a certain reference volume (such as a nucleus of the brainstem or a cortical area). The points may, for example, represent different categories of labelled cells or axonal fields of termination. We say that there is spatial neutrality between points of type 1 and 2 if the types are signed by random labelling. If a mechanism drives the two point categories together, we say that the point patterns are positively associated. Conversely, if a mechanism drives type 1 and 2 points apart, we say that they are segregated. By comparing two cumulative distribution functions of distances between points, we can distinguish neutrality, positive association, and segregation. One function, H12(t), is the cumulative distribution function of the distance t between a pair of randomly selected points of type 1 and 2. The other, H00(t), is the corresponding function for a pair of points randomly selected without reference to type. Plots of the estimated difference between these two functions give an indication of positive association, neutrality, or segregation. A statistical test, based on simulations of random (neutral) distributions, can be used to see whether deviations from neutrality are significant. We apply the analysis described above to a major pathway of the brain, namely the ponto-cerebellar projection. Different types of cells in the pontine nuclei are retrogradely labelled with the fluorescent tracers Rhodamine-B-isothiocyanate, Fluoro-Gold, and Fast Blue. The tracers are injected in adjacent or more distant folia of the cerebellar paraflocculus. The location of the somata of labelled cells are recorded and the total distribution reconstructed in three dimensions and displayed on a dynamic graphics workstation. We ask whether different units (folia) in the paraflocculus receive information from the same population, from two different positively associated populations, or from segregated cell populations. We find a statistically significant tendency for cell populations projecting to adjacent folia to be positively associated, although there are few cells containing multiple labels. Populations of neurons projecting to folia wider apart are significantly segregated. From inspections of the reconstructions, using real-time rotations, we find that the swarms of labelled neurons tend to accumulate in shells or lamellae in the pons. Within the lamellae, the cells are aggregated in clusters and bands with empty holes (containing unlabelled ponto-cerebellar cell bodies, presumably projecting to other cerebellar targets) in between. By determining the average distance to a reference plane for each cell population, we find that cell populations shift in a ventro-medial direction as the injection sites move from the medial part of the dorsal paraflocculus toward the lateral part and into the ventral paraflocculus. We therefore conclude that there is a continuous shift in location of ponto-cerebellar cell populations, corresponding to specific shifts in cerebellar target regions.